Xboxsolution has posted this nifty tidbit of information regarding the ability to access your Xbox Live account after the migration to the Xbox 360:
If you have migrated your XBL account to the 360 you may soon find out something Xbox.com has not posted yet. Your account info is now accessible on the Xbox 360 only! If you try and look at the Account Manager on the regular Xbox you will get an error message. This is not a glitch Microsoft decided to use a new more secure encryption system for your credit card and other information.
We wanted to post this in case you try and see your subscription or any other information from the original Xbox and think there is something wrong. I spoke with a tier 2 tech at Microsoft and they thought this was posted on the site and are making sure it will be soon. So basically once you transfer your account to the 360 it acts as the main console. You will still be able to play and use your original Xbox system and live features you just will not be able to access your account information. We also did not want anyone to discover this and waste hours on hold. Just to find out there is nothing wrong.